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Beliebt Algebra >

3x^4-4x^3+4x^2-4x+1=0

Lösung

3 x^{4} - 4 x^{3} + 4 x^{2} - 4 x + 1 = 0

Lösung

x = 1, x = \frac{1}{3}, x = i, x = - i

Schritte zur Lösung

3 x^{4} - 4 x^{3} + 4 x^{2} - 4 x + 1 = 0

Faktorisiere

3 x^{4} - 4 x^{3} + 4 x^{2} - 4 x + 1 : (x - 1) (3 x - 1) (x^{2} + 1)

(x - 1) (3 x - 1) (x^{2} + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 1 = 0 or 3 x - 1 = 0 or x^{2} + 1 = 0

Löse

x - 1 = 0 : x = 1

Löse

3 x - 1 = 0 : x = \frac{1}{3}

Löse

x^{2} + 1 = 0 : x = i, x = - i

Die Lösungen sind

x = 1, x = \frac{1}{3}, x = i, x = - i

Graph

Beliebte Beispiele

2(x^2-36)(x^2+49)=0

2 (x^{2} - 36) (x^{2} + 49) = 0

x^{3} - 5 x^{2} - x - 1 = 0

x^3-4x^2+7x-1=0

x^{3} - 4 x^{2} + 7 x - 1 = 0

4 x = x^{3} + 3 x^{2}

x (x + 3) (x - 1) = 0